Uncharted Waters is one of those games that suffers mostly from being totally outdone by its sequel, which offers everything that it does on the same platform, but also Better and with Moar Moar. The first game, however, is fairly solid on its own right; it takes a number of cues from Sid Meier's Pirates, but is not nearly the same game. Piracy is possible, but the focus here is much more on trade than combat; until you've built a fairly sizable fortune trading, combat is actually next to impossible with the low-level ships and armaments.
In this one you play as the son of a disgraced Duke in Portugal, determined to rebuild his family's name and fortune through trade. The game doesn't tell you this up front, but you have 20 in-game years to accomplish this task; the victory condition that gets you an ending is to eventually marry the Princess of Portugal. Like a lot of Koei's work, this is one of those "read the manual first" games that explains very little in-game, but once you understand the interface and the overall goals, really isn't super complicated.
If you don't have a manual, however, it can be near impossible to get started, so here's the basic gist. The quickest route to piling up cash is simply buying stuff low in one port and selling it high in another. This usually involves buying stuff in a region where there's a surplus of it, and multiple ports selling it to drive prices down, then taking it somewhere else in the world where it can't be natively produced to sell for a big profit. Cash rules everything around us, even in 1502, but it isn't the lone answer. There's also your reputation to build up; you need to impress the King of Portugal to get titles, and get various missions from him, which culminates in rescuing the Princess from the evil Spaniards, thus allowing you to get all nastay in that pootay. Since you start out as a nobody, however, you can't get missions directly from the King at first; bizzarely, you have to do minor favors for merchants to build this up in the early going. Discovering new ports and successfully sailing the more far-flung and dangerous areas of the world helps this too. Eventually the King will ask you to do some privateering for him, and you're free to attack merchants of other nations, but piracy is very low-reward in this one compared to just trading and running fetch quests when called for.
Unlike the wealth of options for making your way in the world in the sequel, this one sticks you with only one quest possibility at a time. Generally the pattern is, you sail around for a bit making money and exploring however you care to, and while doing this eventually you stop in at a Tavern and hear that someone is looking for you at a certain port. Go to the merchant at that port, and they'll want you to bring them 30 or so barrels of some random good. Do so, and they usually pay you a little more than you'd make normally selling that amount, plus your reputation goes up. Go back to freebooting for a bit until the Tavern gossip/barmaid puts you on to another quest; eventually, the King of Portugal gets mixed into this process and starts calling you directly. On the one hand, this is a bit of a simpler introduction for someone totally new to the series; you only have to worry about being allied to one nation, and have only one quest in front of you at a time. On the other hand, it's a bit more stifling and confining, and there's some hinks that can make the quests annoying or even outright undoable. One early one I ran into is that the merchant at London wanted wool; problem is, London is the only port accessible early in the game that sells wool, and their market is locked off to you while you're on a quest for their merchant. You can cancel out of any quest, fortunately, but your reputation takes a hit and your overall quest for Princess Pootay gets set back a bit. This game also has Seaweed, which I don't recall being in the sequel New Horizons; it's a random disaster that occurs in the deep ocean, particularly in Asia, and basically forces you to reset the game if it happens more than a couple squares off of land, as it just forces all your ships to drift in a circle forever (with no way to repair it unless you can reach shore). Unlike storms, there doesn't seem to be items or figureheads you can buy to ward it off; there's just a random chance of it every time you go through certain areas. Sucks butt.
The graphics are also a bit crummier than the second game, and the interface a bit more simplistic and clunky, though both are still passable. A note about the music - the soundtrack to both this game and the sequel were composed by anime soundtrack legend Yoko Kanno. Judging by the official soundtrack CDs, however, what I think happened was that Ms. Kanno recorded all the music with a combination of high-quality synths and live instruments, then dropped it off at Koei for hapless sound designers to translate to chiptunes. Whoever did that for this first game didn't do the greatest job; the game actually has an amazing soundtrack in its original form, but on the SNES it's ported in a rather heavy-handed and clumsy way, and some of the pieces sound really obnoxious.
I still feel this is a pretty good game on the whole, just kind of pointless to play with the excellence of New Horizons available on nearly every platform that this one appeared on too (save the NES, I think.) Hardcore fans of the series should find it worth their time, though; particularly those of us that don't speak any Asian languages, because this, New Horizons and Uncharted Waters Online are all we've ever gotten of the franchise at this point, and there's no fan translations of any of the others right now that I know of.